Problem: Given $ m \angle MON = 8x - 38$, $ m \angle LOM = 3x - 7$, and $ m \angle LON = 43$, find $m\angle MON$. $O$ $L$ $N$ $M$
Explanation: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Substitute in the expressions that were given for each measure: $ {3x - 7} + {8x - 38} = {43}$ Combine like terms: $ 11x - 45 = 43$ Add $45$ to both sides: $ 11x = 88$ Divide both sides by $11$ to find $x$ $ x = 8$ Substitute $8$ for $x$ in the expression that was given for $m\angle MON$ $ m\angle MON = 8({8}) - 38$ Simplify: $ {m\angle MON = 64 - 38}$ So ${m\angle MON = 26}$.